# Objective

Work out a drag force for a unit sphere traveling through air at velocity. Values for formulae are below. The context of this question is that I am calculating this in an atmospheric environment. So the values provided are for air.

## Information

Through my research I have come across the following information.

### Data

NAME UNIT

Gravity = 9.80665 m/s/s
AirMassDensity = 1.204 kg/m^3
Velocity = 2 m/s

### Formulae

Drag Coefficient: c = 2F \ p * (v * v) * A
Source: http://en.wikipedia.org/wiki/Drag_coefficient#Definition
Where:
c is the coefficient.
F is the drag force.
p is the density of the fluid/gas.
v is the relative velocity.
A is the reference area of the object.

### Problem(s)

A) I don't know what F is in the Drag Coefficient formula. So I would be interested in finding this out, as I do not understand the description given.
B) I could calculate F if c is known, but c is also unknown.
C) As per this http://en.wikipedia.org/wiki/Drag_coefficient (at the bottom) it says that for some shapes, such as spheres, c is solely dependent on the Reynold's Number. It doesn't really go on to explain how and how I could calculate it for use in the Drag Coefficient equation.
D) Is this the correct way to do it, or am I way off? :)

Help/corrections appreciated as I'm stuck at this point unfortunately.

## Misc Info

I'm basically wiring up my own physics simulation in a video game that I am programming for, and am doing this just to learn a little bit more about how forces interact, and advance my mathematics skills. One problem I have come across whilst learning complex things via online, is that often I am unsure what the question is I need to ask. I almost need to understand how physics works before I can ask a physics-related question. So forgive me if my terminology is incorrect, and I am very interested in any corrections to my understanding of the material thus far. Thanks!

• There's so much more to this than you think, like if the ball starts rolling it really is more of a fluid simulation topic. If it's a real-time simulation for use in say a game (where accuracy isn't hugely important) usually you have a wind force, and some drag that will act proportionally to either velocity squared (REMEMBER to take into account the direction when you square!) or just the velocity – Alec Teal Jan 2 '15 at 13:54
• If you take a look at the first half of this answer, you can see the formula being used in practice. – Řídící Jan 2 '15 at 14:02
• Thanks for the input, I am still investigating this and reading other answers. – Ian Smithers Jan 2 '15 at 15:25

OK so after some reading and research I have answered my question with the following - pseudo-code incoming:

// PHASE 1 - GRAVITY FOR THIS OBJECT
position = 0, 0, 0
mass = 1
gravity = 9.80665
fGrav = mass * gravity

// PHASE 2 - DRAG FOR THIS OBJECT
velocity = 0 // Object starts from rest
airMassDensity = 1.204

dragForce = 0.5f * 0.47 * airMassDensity * Dot(velocity, velocity) * area
fDrag = -velocity.normalized * dragForce

// PHASE 3 - ACCUMULATE FORCES (TO BE USED IN CHANGE IN VELOCITY)
forces = fGrav + fDrag;

// PHASE 4 - UPDATE VELOCITY (TO BE USED IN CHANGE IN POSITION)
position += forces * timeDelta


In regards to my questions about calculating c which is the drag coefficient, that involved being a case of using some pre-calculated values, which for a sphere are readily available. I still wish to know how to calculate it for an object, but a lot of replies I got from people indicated its a pretty decent sized subject, and I would be well-advised to use those values available for things. Hope this helps someone in the future!

• The final part is incorrect. F=m*a (Newton) with what a=F/m, so acceleration = forces / mass, considering acceleration constant (from one frame to another, small time delta) velocity = velocity0 + acceleration * timeDelta and position = position0 + velocity0 * timeDelta + 1/2 * acceleration * timeDelta * timeDelta. velocity0 and position0 are the previous ones. – Schcriher Dec 8 '18 at 21:23